A Grassmann Path From AdS_3 to Flat Space
Abstract
We show that interpreting the inverse AdS_3 radius 1/l as a Grassmann variable results in a formal map from gravity in AdS_3 to gravity in flat space. The underlying reason for this is the fact that ISO(2,1) is the Inonu-Wigner contraction of SO(2,2). We show how this works for the Chern-Simons actions, demonstrate how the general (Banados) solution in AdS_3 maps to the general flat space solution, and how the Killing vectors, charges and the Virasoro algebra in the Brown-Henneaux case map to the corresponding quantities in the BMS_3 case. Our results straightforwardly generalize to the higher spin case: the recently constructed flat space higher spin theories emerge automatically in this approach from their AdS counterparts. We conclude with a discussion of singularity resolution in the BMS gauge as an application.
Cite
@article{arxiv.1312.2941,
title = {A Grassmann Path From AdS_3 to Flat Space},
author = {Chethan Krishnan and Avinash Raju and Shubho Roy},
journal= {arXiv preprint arXiv:1312.2941},
year = {2015}
}
Comments
20 pages, 1 figure; v2: many refs added, minor changes, v3: typos fixed, one more ref added, JHEP version